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Merge pull request #6999 from ivq/ecp_doc

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Doc: Add note on special use of A in ecp group structure
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Manuel Pégourié-Gonnard 2023-08-10 08:24:05 +00:00 committed by GitHub
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3 changed files with 51 additions and 4 deletions
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3
ChangeLog.d/improve-doc-on-ecp-curve-optimized-representation.txt Normal file
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@ -0,0 +1,3 @@
Features
* The documentation of mbedtls_ecp_group now describes the optimized
representation of A for some curves. Fixes #8045.

48
include/mbedtls/ecp.h
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@ -197,6 +197,27 @@ mbedtls_ecp_point;
* odd prime as mbedtls_ecp_mul() requires an odd number, and
* mbedtls_ecdsa_sign() requires that it is prime for blinding purposes.
*
* The default implementation only initializes \p A without setting it to the
* authentic value for curves with <code>A = -3</code>(SECP256R1, etc), in which
* case you need to load \p A by yourself when using domain parameters directly,
* for example:
* \code
* mbedtls_mpi_init(&A);
* mbedtls_ecp_group_init(&grp);
* CHECK_RETURN(mbedtls_ecp_group_load(&grp, grp_id));
* if (mbedtls_ecp_group_a_is_minus_3(&grp)) {
* CHECK_RETURN(mbedtls_mpi_sub_int(&A, &grp.P, 3));
* } else {
* CHECK_RETURN(mbedtls_mpi_copy(&A, &grp.A));
* }
*
* do_something_with_a(&A);
*
* cleanup:
* mbedtls_mpi_free(&A);
* mbedtls_ecp_group_free(&grp);
* \endcode
*
* For Montgomery curves, we do not store \p A, but <code>(A + 2) / 4</code>,
* which is the quantity used in the formulas. Additionally, \p nbits is
* not the size of \p N but the required size for private keys.
@ -223,8 +244,11 @@ mbedtls_ecp_point;
typedef struct mbedtls_ecp_group {
mbedtls_ecp_group_id id; /*!< An internal group identifier. */
mbedtls_mpi P; /*!< The prime modulus of the base field. */
mbedtls_mpi A; /*!< For Short Weierstrass: \p A in the equation. For
Montgomery curves: <code>(A + 2) / 4</code>. */
mbedtls_mpi A; /*!< For Short Weierstrass: \p A in the equation. Note that
\p A is not set to the authentic value in some cases.
Refer to detailed description of ::mbedtls_ecp_group if
using domain parameters in the structure.
For Montgomery curves: <code>(A + 2) / 4</code>. */
mbedtls_mpi B; /*!< For Short Weierstrass: \p B in the equation.
For Montgomery curves: unused. */
mbedtls_ecp_point G; /*!< The generator of the subgroup used. */
@ -991,6 +1015,26 @@ int mbedtls_ecp_mul_restartable(mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
mbedtls_ecp_restart_ctx *rs_ctx);
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
/**
* \brief This function checks if domain parameter A of the curve is
* \c -3.
*
* \note This function is only defined for short Weierstrass curves.
* It may not be included in builds without any short
* Weierstrass curve.
*
* \param grp The ECP group to use.
* This must be initialized and have group parameters
* set, for example through mbedtls_ecp_group_load().
*
* \return \c 1 if <code>A = -3</code>.
* \return \c 0 Otherwise.
*/
static inline int mbedtls_ecp_group_a_is_minus_3(const mbedtls_ecp_group *grp)
{
return grp->A.MBEDTLS_PRIVATE(p) == NULL;
}
/**
* \brief This function performs multiplication and addition of two
* points by integers: \p R = \p m * \p P + \p n * \p Q

4
library/ecp.c
View file

@ -1255,7 +1255,7 @@ static int ecp_sw_rhs(const mbedtls_ecp_group *grp,
MPI_ECP_SQR(rhs, X);
/* Special case for A = -3 */
if (grp->A.p == NULL) {
if (mbedtls_ecp_group_a_is_minus_3(grp)) {
MPI_ECP_SUB_INT(rhs, rhs, 3);
} else {
MPI_ECP_ADD(rhs, rhs, &grp->A);
@ -1526,7 +1526,7 @@ static int ecp_double_jac(const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
/* Special case for A = -3 */
if (grp->A.p == NULL) {
if (mbedtls_ecp_group_a_is_minus_3(grp)) {
/* tmp[0] <- M = 3(X + Z^2)(X - Z^2) */
MPI_ECP_SQR(&tmp[1], &P->Z);
MPI_ECP_ADD(&tmp[2], &P->X, &tmp[1]);